The rupee was at 65.3275 to the dollar after falling to 65.3550, its lowest since March 24, on corporate dollar purchases and dollar outflows from equity markets, said dealers. The Indian currency had ended at 65.12 on Monday.
The benchmark BSE index fell 0.5 percent, while the broader NSE index was 0.4 percent lower.
"There is panic among foreign investors on fiscal stimulus and growth," said one dealer at a foreign bank.
India's economic growth slowed to a three-year low of 5.7 percent in the June quarter, prompting the government to plan several steps including fiscal stimulus which would push the fiscal deficit wider than budgeted.
The concerns over weak macroeconomic fundamentals has led to foreign investors pulling out dollars from India's stock markets. So far this month, India has seen a net outflow of $359 million led by a sell-off in stocks.